ECC Cipher Processor Based On Knapsack Algorithm

Abstract

Elliptical Curve Cryptography (ECC) provides a secure means of exchanging keys among communicating hosts using the Diffie Hellmen Key Exchange algorithm.  This paper presents the implementation of ECC by first transforming the message into an affine point on the elliptical curve (EC), and then applying the knapsack algorithm on ECC encrypted message over the finite field gF(p). In ECC we normally start with an affine point called Pm(x,y). This point lies on the elliptic curve. In this paper we have illustrated encryption/decryption involving the ASCII value of the characters constituting the message, and then subjecting it to the knapsack algorithm. Thus the modified plain text has been encrypted by application of the ECC method. The modification of the plain text in conjunction with P_m and application of Knapsack algorithm is the new innovation of this paper. The security of ECC relies on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP), i.e. finding k, given P and Q = kP. The problem is computationally intractable for large values of k.

Keywords: Discrete logarithm, elliptic curve cryptography (ECC), knapsack algorithm, public key cryptography, RSA algorithm